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Syllabus: Matrices, determinants, System of linear equations, Eigenvalues and eigenvectors, LU decomposition.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1 &0&1&0&1&1&1&1&1&2&0&0.9&2
\\\hline\textbf{2 Marks Count} & 2 &1&1&1&1&1&2&1&0&0&0&1&2
\\\hline\textbf{Total Marks} & 5 &2&3&2&3&3&5&3&1&2&\bf{1}&\bf{2.9}&\bf{5}\\\hline
\end{array}}}$$

Highest voted questions in Linear Algebra

11 votes
3 answers
91
Let $A$ be a matrix such that:$A=\begin{pmatrix} -1 & 2\\ 0 & -1 \end{pmatrix}$and $B=A+A^2+A^3+\ldots +A^{50}$. Then which of the following is true?$B^{2}=I$$B^{2}=0$$B^...
10 votes
8 answers
92
Suppose the rank of the matrix$$\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$$is $2$ for some real numbers $a$ and $b$. Then $b$ equals$1$$3$$1/2$$1/3$
10 votes
2 answers
94
If $\text{A}$ and $\text{B}$ are square matrices with same order and $\text{A}$ is symmetric, then $\text{B}^{\text{T}}\text{AB}$ isSkew symmetricSymmetricOrthogonalIdemp...
10 votes
2 answers
95
$\begin{vmatrix} 265 && 240 && 219 \\ 240 && 225 && 198 \\ 219 && 198 && 181 \\ \end{vmatrix} = $$779$$679$$0$$256$
9 votes
2 answers
102
A 3X3 matrix P is such that, P^3 = P. Then the eigenvalues of P are:1) 1, 1, -12) 1, 0.5 + j0.866, 0.5 - j0.8663) 1, -0.5 + j0.866, -0.5 - j0.8664) 0, 1, -1
9 votes
2 answers
103
If $\text{A, B, C}$ are any three matrices, then $\text{A}'+\text{B}'+\text{C}' $ is equal toa null matrix$\text{A + B + C}$$\text{(A + B + C)}'$$\text{-(A + B + C})$
9 votes
2 answers
104
If $\begin{vmatrix} 3 && 3 \\ x && 5 \end{vmatrix} =3$ then the value of $x$ is$2$$3$$4$$5$
8 votes
2 answers
108
8 votes
1 answer
109
You have a matrix $A$ with the factorization:$$A=\underbrace{\left(\begin{array}{ccc}1 & & \\3 & 2 & \\1 & -1 & 2\end{array}\right)}_B \quad \underbrace{\left(\begin{arra...
8 votes
3 answers
110
If $A$ is a $2 \times 2$ matrix such that trace $A = det \ A = 3,$ then what is the trace of $A^{-1}$?$1$$\left(\dfrac{1}{3}\right)$$\left(\dfrac{1}{6}\right)$$\left(\dfr...